vv: "eigenvalue" as "attractor"/: a footnote by heinz von foerster

[lorentzen-nicklaus]

 ... looking, for other reasons, at that article by heinz von foerster
 - "erkenntnistheorien und selbstorganisation" (pp. 133-158 in: s.j. schmidt, 
 ed: der diskurs des radikalen konstruktivismus, 6. aufl., ffm 1994: suhrkamp) - 
 i found an interesting footnote on the term "eigenvalue". after introducing it 
 on page 137 with the words "solutions for such self-referential problems are  
 called 'eigenwerte', following the example of david hilbert, who introduced 
 this label at the turn of the century for solutions of mathematical problems of 
 a similar logical structure" (foerster's example is the sentence 'this sentence 
 has...letters'), he adds in an footnote on page 152 (the translations are my 
 own): "with the new interest in recursive functions some of their qualities 
 were, so to speak, invented again. this had the result that a well established 
 terminology was ignored and replaced by a newer, more stylish one. for 
 instance, in comtemporary literature [the article was first published in 1984, 
 kfl] the notion of 'eigenvalue' is, unfortunately, supplanted by the expression 
 'attractor' as if the eigenvalue had an magnetism towards the sequence's phases 
 (cf. hofstadter, douglas r.: "metamagical themas", in: scientific american 
 january 1981, 22-32; january 1982, 16-28). of eigenvalues which cannot be 
 intuitively predicted one then speaks of as 'strange attractors' etc."      

 please don't ask me for mathematical details! perhaps jody knows more about it. 
 anyway, me thought this could be interesting for some of you.


kfl